In the processes for manufacturing very long, thin tubes to be used, for example, in heat exchangers, or other thermal installations, in general the tubes obtained after various mechanical operations are subjected to a final heat treatment in a furnace at a specified temperature for a specified time. At the time of the thermal treatment the tubes are generally stacked in piles between lateral supports to permit a large number of tubes to be treated at the same time. Experience has shown that when the tubes leave the furnace following this thermal treatment they are no longer rectilinear or straight even if they were trued and straightened before going into the furnace, this loss of straightness being due to creep phenomena during the thermal treatment.